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Related papers: QIP $ \subseteq $ AM(2QCFA)

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Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and the quantum regime, we need to look at computationally secure commitment schemes. In this paper, we…

Quantum Physics · Physics 2011-07-26 André Chailloux , Iordanis Kerenidis , Bill Rosgen

We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…

This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP,…

Computational Complexity · Computer Science 2007-05-23 Hirotada Kobayashi , Keiji Matsumoto

A central problem in quantum computational complexity is how to prevent entanglement-assisted cheating in multi-prover interactive proof systems. It is well-known that the standard oracularization technique completely fails in some proof…

Quantum Physics · Physics 2008-10-06 Tsuyoshi Ito , Hirotada Kobayashi , Keiji Matsumoto

Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…

Quantum Physics · Physics 2023-04-11 Tony Metger , Henry Yuen

This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations…

Quantum Physics · Physics 2012-02-29 Stephen P. Jordan , Hirotada Kobayashi , Daniel Nagaj , Harumichi Nishimura

We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key…

Quantum Physics · Physics 2025-06-23 Le-Ran Liu , Min-Quan He , Dan-Bo Zhang , Z. D. Wang

We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTO '22) also…

Quantum Physics · Physics 2024-05-01 Tony Metger , Anand Natarajan , Tina Zhang

Low degree tests play an important role in classical complexity theory, serving as basic ingredients in foundational results such as $\mathsf{MIP} = \mathsf{NEXP}$ [BFL91] and the PCP theorem [AS98,ALM+98]. Over the last ten years, versions…

Quantum Physics · Physics 2020-11-21 Zhengfeng Ji , Anand Natarajan , Thomas Vidick , John Wright , Henry Yuen

$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…

Quantum Physics · Physics 2015-12-08 Anand Natarajan , Thomas Vidick

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient…

Quantum Physics · Physics 2010-11-17 Michael J. Bremner , Richard Jozsa , Dan J. Shepherd

We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In…

Computational Complexity · Computer Science 2026-01-22 Baocheng Sun , Thomas Vidick

Quantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A.…

Quantum Physics · Physics 2007-05-23 M. V. Panduranga Rao , V. Vinay

This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical…

Quantum Physics · Physics 2008-05-12 Hirotada Kobayashi , Keiji Matsumoto , Tomoyuki Yamakami

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA…

Quantum Physics · Physics 2011-04-20 Shenggen Zheng , Lvzhou Li , Daowen Qiu

The recent MIP*=RE theorem of Ji, Natarajan, Vidick, Wright, and Yuen shows that the complexity class MIP* of multiprover proof systems with entangled provers contains all recursively enumerable languages. Prior work of Grilo, Slofstra, and…

Quantum Physics · Physics 2024-07-31 Kieran Mastel , William Slofstra

We present iSAPP (Imperative Static Analyser for Probabilistic Polynomial Time), a complexity verifier tool that is sound and extensionally complete for the Probabilistic Polynomial Time (PP) complexity class. iSAPP works on an imperative…

Logic in Computer Science · Computer Science 2013-04-12 Jean-Yves Moyen , Paolo Parisen Toldin

The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$, which…

Quantum Physics · Physics 2025-12-15 François Le Gall , Yupan Liu , Qisheng Wang

We present three protocols for verifying all languages: (i) For any unary (binary) language, there is a log-space (linear-space) interactive proof system (IPS); (ii) for any language, there is a constant-space weak-IPS (the non-members may…

Computational Complexity · Computer Science 2018-07-13 Maksims Dimitrijevs , Abuzer Yakaryılmaz

The polynomial-time hierarchy ($\mathrm{PH}$) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as $\mathrm{PH}$ does not collapse). Here, we study whether two…

Computational Complexity · Computer Science 2023-12-29 Sevag Gharibian , Miklos Santha , Jamie Sikora , Aarthi Sundaram , Justin Yirka